Endpoint Calculator
Know one endpoint and the midpoint? Enter their x and y coordinates (negatives and decimals fine) to get the missing endpoint, the move that gets you there, and the full segment length.
Example: with Start point — x₁ 2 · Start point — y₁ 3 · Midpoint — xₘ 5 · Midpoint — yₘ 7 → Endpoint (x₂, y₂): (8, 11).
- The moveΔx = 3, Δy = 4 from start to midpoint — applied twice
- Full segment length10 units (each half is 5)
- Midpoint checkMidpoint of (2, 3) and (8, 11) = (5, 7) ✓
Computed by the calculator below using its default values. Change any input to see your own numbers.
Endpoint formula: (x₂, y₂) = (2xₘ − x₁, 2yₘ − y₁) — the midpoint formula solved for the missing end.
The midpoint formula, run backwards
The midpoint averages two endpoints: xₘ = (x₁ + x₂)/2. If you already know the midpoint and one end, solve for the other: x₂ = 2xₘ − x₁ and y₂ = 2yₘ − y₁. Geometrically, whatever move took you from the start to the midpoint — here Δx = 3, Δy = 4 — gets applied a second time, landing at (8, 11) in the default example.
Watch the signs when coordinates are negative: 2(1) − (−4) = 6, because subtracting a negative pushes the endpoint further, not closer.
Always verify
The built-in check row averages your start point with the computed endpoint. If that average reproduces the midpoint you typed, the answer is verified — the same 10-second habit worth using on a test. The full segment is exactly twice the start-to-midpoint distance, which this page also reports.
How it’s calculated
The midpoint averages coordinates: xₘ = (x₁ + x₂)/2 and yₘ = (y₁ + y₂)/2. Solving for the unknown end gives x₂ = 2xₘ − x₁ and y₂ = 2yₘ − y₁. Segment length = 2·√((xₘ − x₁)² + (yₘ − y₁)²). Coordinates display to 3 decimals.
Assumes the second point you enter really is the midpoint — if it is some other fraction along the segment, the doubling step no longer applies.
Worked examples
| Start | Midpoint | Endpoint |
|---|---|---|
| (0, 0) | (4, 3) | (8, 6) |
| (2, 3) | (5, 7) | (8, 11) |
| (-4, 6) | (1, 2.5) | (6, -1) |
| (10, 0) | (5, 5) | (0, 10) |
Computed with (x₂, y₂) = (2xₘ − x₁, 2yₘ − y₁).
Common mistakes
- Averaging the start and midpoint — that finds the quarter point; the endpoint needs doubling.
- Sign slips with negative coordinates: 2xₘ − x₁ subtracts a negative and grows the result.
- Swapping which point is the start and which is the midpoint — the two roles are not interchangeable.
- Applying the formula to x but forgetting to do the same for y.
Frequently asked questions
What is the endpoint formula?
x₂ = 2xₘ − x₁ and y₂ = 2yₘ − y₁, where (x₁, y₁) is the known endpoint and (xₘ, yₘ) is the midpoint. It is the midpoint formula rearranged to isolate the unknown end.
Why do you double the midpoint?
Because the midpoint is an average: xₘ = (x₁ + x₂)/2. Multiply both sides by 2 and subtract the known x₁, and the unknown x₂ is what remains.
How do I check an endpoint answer?
Average it with the start point: ((x₁ + x₂)/2, (y₁ + y₂)/2). If that reproduces the midpoint you were given, the endpoint is right. This page runs that check automatically.
Does this work with negative or decimal coordinates?
Yes — the algebra is identical anywhere on the plane. Negative inputs just demand care with signs, which is exactly where most hand errors happen.